Dave walked to his friends house at a rate of 4 mph and returned biking at a rate of 10 mph. If it took him 18 minutes longer to walk than bike, what was the total distance of the round trip?
The Correct Answer and Explanation is:
Answer: 12 miles
Explanation
To find the total distance of the round trip, we must determine the distance between Dave’s house and his friend’s house, which we’ll call d miles (one way). Dave walks there at 4 mph and bikes back at 10 mph.
We know:
- Time = Distance ÷ Speed
- It took Dave 18 minutes longer to walk than to bike. Since we’re working with speeds in miles per hour, we convert 18 minutes to hours: 18 minutes=1860=0.3 hours18\ \text{minutes} = \frac{18}{60} = 0.3\ \text{hours}18 minutes=6018=0.3 hours
Let’s write the expressions for time:
- Time to walk to his friend’s house: d4\frac{d}{4}4d
- Time to bike back: d10\frac{d}{10}10d
According to the problem:d4=d10+0.3\frac{d}{4} = \frac{d}{10} + 0.34d=10d+0.3
Now, solve this equation:
- Subtract d10\frac{d}{10}10d from both sides: d4−d10=0.3\frac{d}{4} – \frac{d}{10} = 0.34d−10d=0.3
- Find a common denominator: 5d−2d20=0.3⇒3d20=0.3\frac{5d – 2d}{20} = 0.3 \Rightarrow \frac{3d}{20} = 0.3205d−2d=0.3⇒203d=0.3
- Multiply both sides by 20: 3d=63d = 63d=6
- Divide by 3: d=2d = 2d=2
So, the one-way distance is 2 miles. The total round-trip distance is:2 miles (walked)+2 miles (biked)=4 miles2 \text{ miles (walked)} + 2 \text{ miles (biked)} = 4\ \text{miles}2 miles (walked)+2 miles (biked)=4 miles
Wait! Let’s double-check:
The correct interpretation should be:
- ddd is the one-way distance.
- So, total round trip distance is 2d=42d = 42d=4 miles.
Oops—there’s a mistake here. Let’s rework it:
Back to:d4=d10+0.3⇒3d20=0.3⇒3d=6⇒d=2\frac{d}{4} = \frac{d}{10} + 0.3 \Rightarrow \frac{3d}{20} = 0.3 \Rightarrow 3d = 6 \Rightarrow d = 24d=10d+0.3⇒203d=0.3⇒3d=6⇒d=2
Yes—one way is 2 miles, round trip is 4 miles, not 12 miles.
🔁 Corrected Final Answer: 4 miles.
